My E91 320d needed a top-up after 16k miles, and rear tyres too. Both seem to be normal - all my recent cars have used some oil over time.

I purchased my oil from a main dealer. Cost about £15 for a litre but I know it is the right grade and won't get any warranty hassles. The filler cap says 'BMW recommends Castrol', so this would be okay too I suspect. I think the grade was 0W40 but don't quote me on that.